Solving Rectilinear Problems - Example Problem 2.3-2

 

A car is driving down a straight flat road. The acceleration of the car follows the a-t graph shown. The car starts from rest at t₀ = 0 seconds, reaches its maximum velocity of 45 m/s, and drives at that velocity for 5 seconds. The driver then applies the brakes slowing the car to an eventual stop. At what time does the car stop?

 

 

Given:

• v₀ = 0
• v_B = 45 m/s
• t₂ - t₁ = 5 s

 

Find:

• t_stop

 

Video solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

Interactive solution:

 

Notice that the a-t graph has been labeled in segments.

 

What is the acceleration equation a(t) for segment A?

 

a_A = -10(t/t₁) m/s²
a_A = -10(t/t₁) + 10 m/s²
a_A = 10(t/t₁) + 10 m/s²